Refined modelling of anisotropy influence on the optical gain in Mid-IR quantum cascade lasers

We describe an elaborate model for calculation of optical gain in quantum cascade laser (QCL) taking into account that such complex layered quantum-well based structure should be viewed as an anisotropic material in terms of dielectric constant. The layering induced anisotropy leads to substantial modifications of electron-longitudinal (LO) phonon scattering rates owing to the occurrence of additional resonant frequencies for LO phonons, each affecting the totals scattering rate between relevant subbands. This clearly impacts the carrier distribution between the subbands and alters the degree of population inversion in the active region of a QCL, in comparison to the results of an isotropic permittivity model, as illustrated by our numerical example.